Rig doesn't keep X-Ray enabled when linked into new file
The object properties used will depend on the way you link the object in. If you link an object directly it will honour the external X-Ray setting.

When you link in a group, which contains a mesh and an armature, a local empty object is created which uses DupliGroups to show the mesh and this ignores most of the linked object's settings. Only the properties of the local empty are used, think of the local empty as the parent and the external mesh inherits the parent settings.

When you create a proxy rig, you are creating a new Armature object that is local to the current file, which then uses the external rig data and the external armature's object settings do not get consulted.

An addon could be created that will copy various settings when linking and making a proxy rig, or add a button to copy these properties between the external and local objects. You may also ask a developer to adjust blender so that it copies some of the object properties when linking or making a proxy, which sounds like a reasonable request to me.